The Senate can't make such a rule change unless it pushes through a Constitutional amendment. In Section 2, Article 2, Clause 2, the Constitution requires a two-thirds vote of the Senate to approve treaties.
Agreed, but Congress is seeing this as something 0’ pushes thru the UN, by not calling it a treaty; thus, it is acting with legislation... tiptoeing around the Constitution in tandem with the won. They are complicit.
When there is DC agreement that parts of the Constitution need not apply, they just push forward, stomping on it along the way. Look at Article I Section 8, clearly deliniating what Congress can do... and stomping on that with isolated instances probably back in the 1700’s, ramped up on its stomping thru the 1900’s, and now zooming exponentially with major Constitutional stompings in the 2010’s.